When a three-dimensional object like a rectangular prism is dilated by a scale factor \( k \), the surface area of the new object is affected by the square of the scale factor.
In this case, the scale factor is \( k = 3 \). The surface area of the dilated prism can be calculated using the following formula:
\[ \text{New Surface Area} = k^2 \times \text{Original Surface Area} \]
Where:
- \( k = 3 \) (the scale factor)
- \( \text{Original Surface Area} = 4 , \text{in}^2 \)
Plugging in the values:
\[ \text{New Surface Area} = 3^2 \times 4 , \text{in}^2 = 9 \times 4 , \text{in}^2 = 36 , \text{in}^2 \]
Thus, the surface area of the new dilated rectangular prism is \( \boxed{36 , \text{in}^2} \).
1 answer